A coupled electron diffraction and rigid unit mode (RUM) study of the crystal chemistry of some zeotypic AlPO4 compounds

Electron diffraction and lattice dynamical calculations are used to investigate the unit cells, space group symmetries and inherent displacive flexibility of the room-temperature average structures of AlPO4-8, AlPO4-16 and AlPO4-tridymite. The zero-frequency rigid unit modes (RUMs) of the idealized high-symmetry polymorphs thereof are also investigated along with their relationship to the lower-temperature polymorphism of these zeotypic aluminophosphates. The clear presence of image satellite reflections in addition to the Bragg reflections (G) of the underlying Cmc21 parent structure in the case of AlPO4-8 shows that the true unit cell of the room-temperature polymorph has a doubled c-axis due to a condensed RUM mode. Structured diffuse scattering is also observed which can be related to the thermal excitation of RUM modes. In the case of AlPO4-tridymite, a complex F1 triclinic polymorph is observed and related to soft RUM modes while, in the case of AlPO4-16, a soft q=0 RUM mode is shown to be responsible for an observed phase transition in the case of the all SiO2 analogue of AlPO4-16. A large number of additional zero-frequency RUM modes also exist in the case of AlPO4-16.